CN114301361B - A control method for electrolytic capacitor-free permanent magnet synchronous motor drive system based on bus current control - Google Patents

A control method for electrolytic capacitor-free permanent magnet synchronous motor drive system based on bus current control Download PDF

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CN114301361B
CN114301361B CN202111575725.XA CN202111575725A CN114301361B CN 114301361 B CN114301361 B CN 114301361B CN 202111575725 A CN202111575725 A CN 202111575725A CN 114301361 B CN114301361 B CN 114301361B
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章玮
梁晨
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Zhejiang University ZJU
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Abstract

The invention discloses a control method of a permanent magnet synchronous motor driving system without electrolytic capacitor based on bus current control, which comprises the following steps: directly calculating a q-axis voltage given value of the motor according to constraint conditions between the bus current command value and motor variables; based on Lyapunov stability theory, carrying out convergence judgment on the motor current under the q-axis given voltage, if the motor current is judged to be non-convergence, obtaining a motor q-axis current command value according to the approximate relation between a bus current command value and the motor q-axis current, and calculating a motor q-axis voltage given value based on a feedback linearization idea; and carrying out coordinate transformation on the given voltage of the d-q axes of the motor and outputting the voltage to the motor through the SVPWM module. The method has the advantages of high motor efficiency, high network side power factor, easy realization of control strategies and strong system robustness, and the network side power factor control effect is little influenced by system parameter errors.

Description

一种基于母线电流控制的无电解电容永磁同步电机驱动系统 控制方法An electrolytic capacitor-free permanent magnet synchronous motor drive system based on bus current control Control Method

技术领域Technical field

本发明属于电机控制领域,尤其涉及无电解电容永磁同步电机驱动系统控制技术。The invention belongs to the field of motor control, and in particular relates to electrolytic capacitor-free permanent magnet synchronous motor drive system control technology.

背景技术Background technique

永磁同步电机以其高效率、高功率密度等特点被广泛应用于工业和家电中。然而传统交-直-交永磁同步电机变频驱动系统中采用的直流母线电解电容会降低系统可靠性并且恶化网侧输入功率因数。为了满足网侧输入功率要求,又需要增加功率因数校正电路。因此,用薄膜电容代替母线电解电容并采用控制策略提高网侧输入功率因数的研究得到了广泛的关注。Permanent magnet synchronous motors are widely used in industry and home appliances due to their high efficiency and high power density. However, the DC bus electrolytic capacitors used in traditional AC-DC-AC permanent magnet synchronous motor variable frequency drive systems will reduce system reliability and worsen the grid-side input power factor. In order to meet the grid-side input power requirements, a power factor correction circuit needs to be added. Therefore, research on using film capacitors to replace bus electrolytic capacitors and using control strategies to improve grid-side input power factor has received widespread attention.

目前存在的无电解电容永磁同步电机驱动系统控制方法通过采用重复控制器、比例谐振控制器等方式实现对功率、电流的控制以提高网侧功率因数,但存在着控制效果不佳、控制器参数整定困难、电机效率较低的问题。The currently existing electrolytic capacitor-free permanent magnet synchronous motor drive system control method uses repetitive controllers, proportional resonance controllers, etc. to control power and current to improve grid-side power factor. However, there are problems such as poor control effect and controller Problems such as difficulty in parameter tuning and low motor efficiency.

发明内容Contents of the invention

为了解决上述技术问题,本发明提供了一种基于母线电流控制的无电解电容永磁同步电机驱动系统控制方法,其基于系统收敛性分析直接控制母线电流,系统复杂度低鲁棒性强、能实现网侧高功率因数,并基于最小铜耗原则计算电机d轴电流指令,有效提高了电机效率。In order to solve the above technical problems, the present invention provides an electrolytic capacitor-free permanent magnet synchronous motor drive system control method based on bus current control, which directly controls the bus current based on system convergence analysis, has low system complexity, strong robustness, and can Achieving high power factor on the grid side and calculating the motor d-axis current command based on the minimum copper loss principle effectively improves motor efficiency.

本发明的目的是通过以下技术方案来实现:一种基于母线电流控制的无电解电容永磁同步电机驱动系统控制方法,包括以下步骤:The object of the present invention is to be achieved through the following technical solutions: a control method for a non-electrolytic capacitor permanent magnet synchronous motor drive system based on bus current control, which includes the following steps:

先根据母线电流指令值与电机变量间的约束条件得到电机q轴电压给定值/> First, according to the bus current command value The constraints between the motor variables and the motor variables are used to obtain the motor q-axis voltage given value/>

然后基于李雅普诺夫稳定性理论对所述电机q轴电压给定值下的电机电流进行收敛性分析;若判断为收敛,则采用所述电机q轴电压给定值/>若判断为非收敛,则根据所述母线电流指令值/>与电机q轴电流间的近似关系得出电机q轴电流指令值/>并基于反馈线性化思想得到电机q轴电压给定值/> Then based on Lyapunov stability theory, the q-axis voltage of the motor is given a given value Carry out convergence analysis on the motor current below; if it is judged to be convergent, the motor q-axis voltage given value/> If it is determined to be non-convergent, the bus current command value/> The approximate relationship with the motor q-axis current results in the motor q-axis current command value/> And based on the feedback linearization idea, the motor q-axis voltage given value/>

最后将电机d轴电压给定q轴电压给定/>进行坐标变换得到静止两相坐标系下的电压给定值/>再将电压输出至电机。Finally, the motor d-axis voltage is given Q-axis voltage given/> Perform coordinate transformation to obtain the voltage given value in the stationary two-phase coordinate system/> Then output the voltage to the motor.

进一步的,所述母线电流指令值根据速度调节器输出值、网侧电压相位和母线电容值得到。Further, the bus current command value Obtained according to the speed regulator output value, grid side voltage phase and bus capacitance value.

进一步的,所述母线电流指令值计算方法包括以下步骤:Further, the bus current command value The calculation method includes the following steps:

先将网侧电压波形进行锁相后得到网侧电压相位角θsFirst, phase-lock the grid-side voltage waveform to obtain the grid-side voltage phase angle θ s ;

然后将电机转速指令值与实际转速作差后经速度调节器输出网侧输入电流指令幅值结合网侧电压相位角θs得到网侧输入电流指令瞬时值/>最后将网侧输入电流指令瞬时值/>减去电容电流瞬时值ic得到母线电流指令值/> Then, the difference between the motor speed command value and the actual speed is made, and then the grid-side input current command amplitude is output through the speed regulator. Combined with the grid-side voltage phase angle θ s, the grid-side input current command instantaneous value/> Finally, input the instantaneous value of the current command on the grid side/> Subtract the instantaneous value of capacitor current i c to obtain the bus current command value/>

进一步的,所述d轴电流指令值基于最小铜耗原则计算,所述d轴电压给定值/>由电流调节器得到。Further, the d-axis current command value Calculated based on the minimum copper loss principle, the d-axis voltage given value/> obtained from the current regulator.

进一步的,所述d轴电流指令值为常数,由于无电解电容驱动系统电机q轴电流为周期正弦波,基于最小铜耗原则获得的d轴电流指令常数值/>计算方法包括以下步骤:Further, the d-axis current command value is a constant. Since the q-axis current of the motor in the electrolytic capacitor-free drive system is a periodic sine wave, the d-axis current command constant value is obtained based on the minimum copper loss principle/> The calculation method includes the following steps:

先作拉格朗日函数其中:First make the Lagrangian function in:

为目标函数,表示系统铜耗,式中id为电机d轴电流,iqrms为电机q轴电流有效值;/>为系统转矩约束条件,式中Ld,Lq分别为电机d-q轴电感,/>为电机永磁体磁链,iqav为电机q轴电流平均值,T为电机平均负载转矩;为电机q轴电流有效值与平均值间的约束条件;λ1,λ2为拉格朗日乘数; is the objective function, representing the system copper loss, where i d is the motor d-axis current, i qrms is the motor q-axis current effective value;/> is the system torque constraint condition, where L d and L q are the motor dq axis inductance respectively,/> is the motor permanent magnet flux linkage, i qav is the average value of the motor q-axis current, and T is the average load torque of the motor; is the constraint condition between the effective value and the average value of the motor q-axis current; λ 1 and λ 2 are Lagrange multipliers;

然后令拉格朗日函数F(id,iqrms,iqav12)对各变量的一阶偏导数等于零,得:Then let the first-order partial derivative of the Lagrangian function F(i d ,i qrms ,i qav12 ) with respect to each variable equal to zero, we get:

最后由式(1)中五个方程组可解出最小铜耗控制对应的d轴电流id,并将其作为d轴指令值表达式为:Finally, the d-axis current i d corresponding to the minimum copper loss control can be solved from the five equations in equation (1) and used as the d-axis command value. The expression is:

进一步的,得到所述电机q轴电压给定值的方法包括以下步骤:Further, obtain the given value of the motor q-axis voltage The method includes the following steps:

先将静止三相坐标系下逆变器调制比函数表示为:First, the inverter modulation ratio function in the stationary three-phase coordinate system is expressed as:

式中:Am为逆变器调制比幅值,θe为电机d轴超前电机a相相轴的角度值;为逆变器输出相角超前电机d轴的角度值;In the formula: A m is the modulation ratio amplitude of the inverter, θ e is the angle value of the motor d-axis leading the motor a-phase axis; It is the angle value of the inverter output phase angle leading the d-axis of the motor;

将静止三相坐标系下电机电压ua、ub、uc用逆变器传递函数Fd与母线电压udc表示为:The motor voltage u a , u b , and u c in the static three-phase coordinate system are expressed by the inverter transfer function F d and the bus voltage u dc as:

[ua ub uc]T=Fd·udc (3);[u a u b u c ] T =F d ·u dc (3);

用静止三相坐标系下电机电流ia、ib、ic与逆变器传递函数Fd将母线电流idc表示为:Using the motor currents i a , ib , ic and the inverter transfer function F d in the static three-phase coordinate system, the bus current i dc is expressed as:

idc=Fd T·[ia ib ic]T (4);i dc = F d T ·[i a i b i c ] T (4);

将式(3)与式(4)通过静止三相坐标系到旋转两相坐标系的恒幅值变换后,得到旋转坐标系下电机电压ud-q,母线电流idc与逆变器调制比矢量间关系为:After transforming equations (3) and (4) through the constant amplitude transformation from the stationary three-phase coordinate system to the rotating two-phase coordinate system, the motor voltage u dq , bus current i dc and inverter modulation ratio vector in the rotating coordinate system are obtained. The relationship between them is:

式中:Im为电机电流幅值;为电机电流相角超前电机d轴的角度值;/>为电机电流矢量;Ad、Aq分别为逆变器调制比矢量/>在d-q坐标系下的分量;In the formula: I m is the motor current amplitude; It is the angle value of the motor current phase angle leading the motor d-axis;/> is the motor current vector; A d and A q are the inverter modulation ratio vectors/> Component in the dq coordinate system;

然后根据式(6)可作图,由图得调制比矢量在电机电流矢量/>上的投影长度L计算公式为:Then a graph can be drawn according to equation (6), and the modulation ratio vector can be obtained from the graph In the motor current vector/> The calculation formula of the projection length L on is:

调制比矢量所在的垂线与d-q轴坐标系交点的坐标值分别为:modulation ratio vector The coordinate values of the intersection points of the vertical line and the dq-axis coordinate system are:

最后由式(5)得调制比矢量的d轴分量/>根据相似三角形关系得再根据式(5)得到电机q轴电压给定值/> Finally, the modulation ratio vector is obtained from equation (5) d-axis component/> According to the similar triangle relationship, we can get Then according to equation (5), the motor q-axis voltage given value/>

进一步的,电机电流收敛性判断方法包括如下步骤:Further, the motor current convergence judgment method includes the following steps:

先将永磁同步电机在d-q坐标系下的电压方程分别表示为:First, the voltage equations of the permanent magnet synchronous motor in the d-q coordinate system are expressed as:

式中:R为定子电阻;ωe为电机电角速度。In the formula: R is the stator resistance; ω e is the electrical angular speed of the motor.

然后将计算得到的电机q轴电压给定带入电机电压方程式(9),化简得:Then the calculated q-axis voltage of the motor is given Enter the motor voltage equation (9) and simplify it to:

根据电机d-q轴电流关系化简得到电机q轴电流的状态变量方程为:According to the simplified relationship between the d-q axis current of the motor, the state variable equation of the q-axis current of the motor is:

基于李雅普诺夫直接方法分析式(11)所示非线性方程稳定性:令等于零,可求得系统存在两个平衡点,分别为:Analyze the stability of the nonlinear equation shown in equation (11) based on Lyapunov direct method: Let is equal to zero, it can be found that the system has two equilibrium points, which are:

系统正常运行时电机q轴电流为正,应保证系统存在正平衡点,即系统需满足/>取正平衡点iq_0进行收敛性判断: When the system is running normally, the motor q-axis current is positive, and it should be ensured that there is a positive balance point in the system, that is, the system needs to satisfy/> Take the positive equilibrium point i q_0 for convergence judgment:

为方便分析,将y=iq-iq_0带入上述方程,使平衡点变成状态空间零点,得变换后方程:For the convenience of analysis, y=i q -i q_0 is brought into the above equation, so that the equilibrium point becomes the zero point of the state space, and the transformed equation is obtained:

将式(11)带入式(13)化简得:Put equation (11) into equation (13) and simplify it:

构造正定李雅普诺夫函数易得当y>-iq_0时李雅普诺夫函数的导数恒小于零,这时可保证系统稳定运行;Construct a positive definite Lyapunov function It is easy to get the derivative of Lyapunov function when y>-i q_0 is always less than zero, then the stable operation of the system can be ensured;

若系统不满足与y>-iq_0这两个收敛条件时,由电机q轴电流与母线电流间的近似关系得到电机q轴电流指令值/>将电机q轴电压方程(9)改写为:/>根据反馈线性化思想,令/>并带入电机q轴电压方程,化简得/>再令控制率/>化简得/>式中a为一正常数,/>为电流误差,可知电流指令与实际电流间的误差随时间收敛至零。If the system does not satisfy With the two convergence conditions y>-i q_0 , the motor q-axis current command value is obtained from the approximate relationship between the motor q-axis current and the bus current/> Rewrite the motor q-axis voltage equation (9) as:/> According to the feedback linearization idea, let/> And bring it into the motor q-axis voltage equation and simplify it to get/> Reorder control rate/> Simplify/> where a is a positive constant,/> is the current error. It can be seen that the error between the current command and the actual current converges to zero over time.

进一步的,最后将电机d轴电压给定q轴电压给定/>进行坐标变换得到静止两相坐标系下的电压给定值/>再通过SVPWM模块将电压输出至电机。Further, finally the motor d-axis voltage is given Q-axis voltage given/> Perform coordinate transformation to obtain the voltage given value in the stationary two-phase coordinate system/> The voltage is then output to the motor through the SVPWM module.

本发明的有益效果是:本发明可用于所有无电解电容永磁同步电机驱动系统中。与现有技术相比,本发明基于最小铜耗原则得到电机d轴电流,提高了电机效率;根据母线电流指令值与电机变量间的约束条件直接计算电机q轴电压给定值,能实现网侧高功率因数,且网侧功率因数控制效果受系统参数误差影响小,整体控制策略易实现,系统鲁棒性强。The beneficial effects of the present invention are: the present invention can be used in all electrolytic capacitor-free permanent magnet synchronous motor drive systems. Compared with the existing technology, the present invention obtains the d-axis current of the motor based on the principle of minimum copper loss, which improves the efficiency of the motor; directly calculates the given value of the q-axis voltage of the motor based on the constraints between the bus current command value and the motor variables, and can realize the network The power factor on the side is high, and the power factor control effect on the grid side is less affected by system parameter errors. The overall control strategy is easy to implement and the system is highly robust.

附图说明Description of the drawings

图1为本发明一实施例中无电解电容驱动系统拓扑结构框图;Figure 1 is a topological block diagram of an electrolytic capacitor-free drive system in an embodiment of the present invention;

图2为本发明一实施例中逆变器调制比矢量计算框图;Figure 2 is a block diagram of the inverter modulation ratio vector calculation in one embodiment of the present invention;

图3为本发明一实施例中仿真d-q轴电流波形;Figure 3 is a simulated d-q axis current waveform in an embodiment of the present invention;

图4为本发明一实施例中仿真网侧输入电流波形。Figure 4 is a simulated grid-side input current waveform in an embodiment of the present invention.

具体实施方式Detailed ways

下面根据附图详细说明本发明,以使本发明的目的和效果变得更加明显。The present invention will be described in detail below based on the accompanying drawings to make the purpose and effects of the present invention more apparent.

在一实施例中,提供了一种基于母线电流控制的无电解电容永磁同步电机驱动系统控制方法,包括以下步骤:In one embodiment, a control method for an electrolytic capacitor-free permanent magnet synchronous motor drive system based on bus current control is provided, including the following steps:

先根据母线电流指令值与电机变量间的约束条件得到电机q轴电压给定值/> First, according to the bus current command value The constraints between the motor variables and the motor variables are used to obtain the motor q-axis voltage given value/>

然后基于李雅普诺夫稳定性理论对电机q轴电压给定值下的电机电流进行收敛性分析;若判断为收敛,则采用电机q轴电压给定值/>若判断为非收敛,则根据母线电流指令值/>与电机q轴电流间的近似关系得出电机q轴电流指令值/>并基于反馈线性化思想得到电机q轴电压给定值/> Then based on Lyapunov stability theory, the motor q-axis voltage is given a given value Carry out convergence analysis on the motor current below; if it is judged to be convergent, the motor q-axis voltage given value/> If it is judged as non-convergence, the bus current command value/> The approximate relationship with the motor q-axis current results in the motor q-axis current command value/> And based on the feedback linearization idea, the motor q-axis voltage given value/>

最后将电机d轴电压给定q轴电压给定/>进行坐标变换得到静止两相坐标系下的电压给定值/>再将电压输出至电机。Finally, the motor d-axis voltage is given Q-axis voltage given/> Perform coordinate transformation to obtain the voltage given value in the stationary two-phase coordinate system/> Then output the voltage to the motor.

在一实施例中,母线电流指令值根据速度调节器输出值、网侧电压相位和母线电容值得到。In one embodiment, the bus current command value Obtained according to the speed regulator output value, grid side voltage phase and bus capacitance value.

在一实施例中,母线电流指令值计算方法包括以下步骤:In one embodiment, the bus current command value The calculation method includes the following steps:

先将网侧电压波形进行锁相后得到网侧电压相位角θsFirst, phase-lock the grid-side voltage waveform to obtain the grid-side voltage phase angle θ s ;

然后将电机转速指令值与实际转速作差后经速度调节器输出网侧输入电流指令幅值结合网侧电压相位角θs得到网侧输入电流指令瞬时值/>最后将网侧输入电流指令瞬时值/>减去电容电流瞬时值ic得到母线电流指令值/> Then, the difference between the motor speed command value and the actual speed is made, and then the grid-side input current command amplitude is output through the speed regulator. Combined with the grid-side voltage phase angle θ s, the grid-side input current command instantaneous value/> Finally, input the instantaneous value of the current command on the grid side/> Subtract the instantaneous value of capacitor current i c to obtain the bus current command value/>

在一实施例中,,d轴电流指令值基于最小铜耗原则计算,d轴电压给定值/>由电流调节器得到。In one embodiment, the d-axis current command value Calculated based on the minimum copper loss principle, d-axis voltage given value/> obtained from the current regulator.

进一步的,d轴电流指令值为常数,由于无电解电容驱动系统电机q轴电流为周期正弦波,基于最小铜耗原则获得的d轴电流指令常数值/>计算方法包括以下步骤:Further, the d-axis current command value is a constant. Since the q-axis current of the motor in the electrolytic capacitor-free drive system is a periodic sine wave, the d-axis current command constant value is obtained based on the minimum copper loss principle/> The calculation method includes the following steps:

先作拉格朗日函数其中:First make the Lagrangian function in:

为目标函数,表示系统铜耗,式中id为电机d轴电流,iqrms为电机q轴电流有效值;/>为系统转矩约束条件,式中Ld,Lq分别为电机d-q轴电感,/>为电机永磁体磁链,iqav为电机q轴电流平均值,T为电机平均负载转矩;为电机q轴电流有效值与平均值间的约束条件;λ1,λ2为拉格朗日乘数; is the objective function, representing the system copper loss, where i d is the motor d-axis current, i qrms is the motor q-axis current effective value;/> is the system torque constraint condition, where L d and L q are the motor dq axis inductance respectively,/> is the motor permanent magnet flux linkage, i qav is the average value of the motor q-axis current, and T is the average load torque of the motor; is the constraint condition between the effective value and the average value of the motor q-axis current; λ 1 and λ 2 are Lagrange multipliers;

然后令拉格朗日函数F(id,iqrms,iqav12)对各变量的一阶偏导数等于零,得:Then let the first-order partial derivative of the Lagrangian function F(i d ,i qrms ,i qav12 ) with respect to each variable equal to zero, we get:

最后由式(1)中五个方程组可解出最小铜耗控制对应的d轴电流id,并将其作为d轴指令值表达式为:Finally, the d-axis current i d corresponding to the minimum copper loss control can be solved from the five equations in equation (1) and used as the d-axis command value. The expression is:

在一实施例中,得到电机q轴电压给定值的方法包括以下步骤:In one embodiment, the motor q-axis voltage given value is obtained The method includes the following steps:

先将静止三相坐标系下逆变器调制比函数表示为:First, the inverter modulation ratio function in the stationary three-phase coordinate system is expressed as:

式中:Am为逆变器调制比幅值,θe为电机d轴超前电机a相相轴的角度值;为逆变器输出相角超前电机d轴的角度值;In the formula: A m is the modulation ratio amplitude of the inverter, θ e is the angle value of the motor d-axis leading the motor a-phase axis; It is the angle value of the inverter output phase angle leading the d-axis of the motor;

将静止三相坐标系下电机电压ua、ub、uc用逆变器传递函数Fd与母线电压udc表示为:The motor voltage u a , u b , and u c in the static three-phase coordinate system are expressed by the inverter transfer function F d and the bus voltage u dc as:

[ua ub uc]T=Fd·udc (3);用静止三相坐标系下电机电流ia、ib、ic与逆变器传递函数Fd将母线电流idc表示为:[u a u b u c ] T = F d · u dc (3); The bus current i dc is represented by the motor currents i a , ib , ic and the inverter transfer function F d in the static three-phase coordinate system . for:

idc=Fd T·[ia ib ic]T (4);i dc = F d T ·[i a i b i c ] T (4);

将式(3)与式(4)通过静止三相坐标系到旋转两相坐标系的恒幅值变换后,得到旋转坐标系下电机电压ud-q,母线电流idc与逆变器调制比矢量间关系为:After transforming equations (3) and (4) through the constant amplitude transformation from the stationary three-phase coordinate system to the rotating two-phase coordinate system, the motor voltage u dq , bus current i dc and inverter modulation ratio vector in the rotating coordinate system are obtained. The relationship between them is:

式中:Im为电机电流幅值;为电机电流相角超前电机d轴的角度值;/>为电机电流矢量;Ad、Aq分别为逆变器调制比矢量/>在d-q坐标系下的分量;In the formula: I m is the motor current amplitude; It is the angle value of the motor current phase angle leading the motor d-axis;/> is the motor current vector; A d and A q are the inverter modulation ratio vectors/> Component in the dq coordinate system;

然后根据式(6)可作图2,由图2得调制比矢量在电机电流矢量/>上的投影长度L计算公式为:Then according to equation (6), Figure 2 can be drawn, and the modulation ratio vector can be obtained from Figure 2 In the motor current vector/> The calculation formula of the projection length L on is:

调制比矢量所在的垂线与d-q轴坐标系交点的坐标值分别为:modulation ratio vector The coordinate values of the intersection points of the vertical line and the dq-axis coordinate system are:

最后由式(5)得调制比矢量的d轴分量/>根据相似三角形关系得再根据式(5)得到电机q轴电压给定值/> Finally, the modulation ratio vector is obtained from equation (5) d-axis component/> According to the similar triangle relationship, we can get Then according to equation (5), the motor q-axis voltage given value/>

在一实施例中,,电机电流收敛性判断方法包括如下步骤:In one embodiment, the motor current convergence judgment method includes the following steps:

先将永磁同步电机在d-q坐标系下的电压方程分别表示为:First, the voltage equations of the permanent magnet synchronous motor in the d-q coordinate system are expressed as:

式中:R为定子电阻;ωe为电机电角速度。In the formula: R is the stator resistance; ω e is the electrical angular speed of the motor.

然后将计算得到的电机q轴电压给定带入电机电压方程式(9),化简得:Then the calculated q-axis voltage of the motor is given Enter the motor voltage equation (9) and simplify it to:

根据电机d-q轴电流关系化简得到电机q轴电流的状态变量方程为:According to the simplified relationship between the d-q axis current of the motor, the state variable equation of the q-axis current of the motor is:

基于李雅普诺夫直接方法分析式(11)所示非线性方程稳定性:令等于零,可求得系统存在两个平衡点,分别为:Analyze the stability of the nonlinear equation shown in equation (11) based on Lyapunov direct method: Let Equal to zero, it can be found that the system has two equilibrium points, which are:

系统正常运行时电机q轴电流为正,应保证系统存在正平衡点,即系统需满足/>取正平衡点iq_0进行收敛性判断: When the system is running normally, the motor q-axis current is positive, and it should be ensured that there is a positive balance point in the system, that is, the system needs to satisfy/> Take the positive equilibrium point i q_0 for convergence judgment:

为方便分析,将y=iq-iq_0带入上述方程,使平衡点变成状态空间零点,得变换后方程:将For the convenience of analysis, y=i q -i q_0 is brought into the above equation, so that the equilibrium point becomes the zero point of the state space, and the transformed equation is obtained:

将式(11)带入式(13)化简得:Put equation (11) into equation (13) and simplify it:

构造正定李雅普诺夫函数易得当y>-iq_0时李雅普诺夫函数的导数恒小于零,这时可保证系统稳定运行;Construct a positive definite Lyapunov function It is easy to get the derivative of Lyapunov function when y>-i q_0 is always less than zero, then the stable operation of the system can be ensured;

若系统不满足与y>-iq_0这两个收敛条件时,由电机q轴电流与母线电流间的近似关系得到电机q轴电流指令值/>将电机q轴电压方程(9)改写为:/>根据反馈线性化思想,令/>并带入电机q轴电压方程,化简得/>再令控制率/>化简得/>式中a为一正常数,/>为电流误差,可知电流指令与实际电流间的误差随时间收敛至零。If the system does not satisfy With the two convergence conditions y>-i q_0 , the motor q-axis current command value is obtained from the approximate relationship between the motor q-axis current and the bus current/> Rewrite the motor q-axis voltage equation (9) as:/> According to the feedback linearization idea, let/> And bring it into the motor q-axis voltage equation and simplify it to get/> Reorder control rate/> Simplify/> where a is a positive constant,/> is the current error. It can be seen that the error between the current command and the actual current converges to zero over time.

在一实施例中,最后将电机d轴电压给定q轴电压给定/>进行坐标变换得到静止两相坐标系下的电压给定值/>再通过SVPWM模块将电压输出至电机。In one embodiment, finally the motor d-axis voltage is given Q-axis voltage given/> Perform coordinate transformation to obtain the voltage given value in the stationary two-phase coordinate system/> The voltage is then output to the motor through the SVPWM module.

工作时,将电机转速指令值与实际转速作差得到电机转速误差,将误差值通过电机速度调节器得到网侧输入电流指令幅值其中,速度调节器可采用PI调节器。During operation, the motor speed error is obtained by making the difference between the motor speed command value and the actual speed. The error value is passed through the motor speed regulator to obtain the grid-side input current command amplitude. Among them, the speed regulator can use a PI regulator.

网侧输入电流指令幅值结合网侧电压相位角θs得到网侧输入电流指令瞬时值其中,网侧电压相位角θs可采用二阶广义积分锁相环(SOGI-PLL)得到,网侧输入电流指令幅值具体计算公式为/> Grid side input current command amplitude Combined with the grid-side voltage phase angle θ s , the grid-side input current command instantaneous value is obtained Among them, the grid-side voltage phase angle θ s can be obtained by using a second-order generalized integral phase-locked loop (SOGI-PLL). The specific calculation formula for the grid-side input current command amplitude is/>

由图1可知,将网侧输入电流指令瞬时值减去电容电流瞬时值ic得到母线电流指令值/>其中,电容电流瞬时值/>式中Cdc为母线电容值;母线电流指令值 As can be seen from Figure 1, the instantaneous value of the grid-side input current command Subtract the instantaneous value of capacitor current i c to obtain the bus current command value/> Among them, the instantaneous value of the capacitor current/> In the formula, C dc is the bus capacitance value; the bus current command value

由公式得到电机d轴电流指令值/>其中,电机q轴电流平均值iqav由滑窗滤波器求平均得到:/>式中N为一个母线电压周期的采样次数,iq(k)表示第k次采样的q轴电流iqBy formula Get the motor d-axis current command value/> Among them, the average value of the motor q-axis current i qav is obtained by averaging the sliding window filter:/> In the formula, N is the number of sampling times in one bus voltage cycle, and i q (k) represents the q-axis current i q sampled at the kth time.

将电机d轴电流指令值与实际电流作差后经过电流调节器得到d轴电压给定值其中,电流调节器可采用PI调节器。The difference between the motor d-axis current command value and the actual current is used to obtain the d-axis voltage given value through the current regulator. Among them, the current regulator can use a PI regulator.

由母线电流指令值与电机电流幅值Im得到调制比矢量/>在电机电流矢量/>上的投影长度L,具体计算方法为/> From the bus current command value Combined with the motor current amplitude I m to obtain the modulation ratio vector/> In the motor current vector/> The projection length L on

由正余弦函数关系得到调制比矢量所在的垂线与d-q轴坐标系交点的坐标值分别为:/> The modulation ratio vector is obtained from the sine and cosine function relationship. The coordinate values of the intersection points of the vertical line and the dq-axis coordinate system are:/>

由电机d轴电压给定值得到调制比矢量/>的d轴分量/> The given value is given by the motor d-axis voltage Get the modulation ratio vector/> d-axis component/>

根据图2所示相似三角形关系得到调制比矢量的q轴分量/> The modulation ratio vector is obtained according to the similar triangle relationship shown in Figure 2 q-axis component/>

最后由调制比矢量的q轴分量/>与母线电压udc得到q轴电压给定值/> Finally, the modulation ratio vector q-axis component/> Combined with the bus voltage u dc , we get the q-axis voltage given value/>

通过与y>-iq_0两个条件判断电机电流是否收敛。若两式不能同时满足时,则需改变q轴电压给定值/>具体方法为:pass Two conditions with y>-i q_0 determine whether the motor current converges. If the two equations cannot be satisfied at the same time, the q-axis voltage given value needs to be changed/> The specific methods are:

由电机q轴电流与母线电流间关系得到q轴电流指令值 The q-axis current command value is obtained from the relationship between the motor q-axis current and the bus current.

根据反馈线性化思想得到q轴电压给定值 Obtain the q-axis voltage given value based on the feedback linearization idea

将电机d轴电压给定q轴电压给定/>进行坐标变换得到静止两相坐标系下的电压给定值/>再通过SVPWM模块将给定电压输出至电机。Give the motor d-axis voltage Q-axis voltage given/> Perform coordinate transformation to obtain the voltage given value in the stationary two-phase coordinate system/> Then the given voltage is output to the motor through the SVPWM module.

本发明可用于所有无电解电容永磁同步电机驱动系统中。与现有技术相比,本发明基于最小铜耗原则得到电机d轴电流,提高了电机效率;根据母线电流指令值与电机变量间的约束条件直接计算电机q轴电压给定值,能实现网侧高功率因数,且网侧功率因数控制效果受系统参数误差影响小,整体控制策略易实现,系统鲁棒性强。功率因数控制效果如图3与图4所示,在q轴电流收敛区域内,网侧输入电流为标准的正弦波,从而最大化了网侧功率因数。The invention can be used in all electrolytic capacitor-free permanent magnet synchronous motor drive systems. Compared with the existing technology, the present invention obtains the d-axis current of the motor based on the principle of minimum copper loss, which improves the efficiency of the motor; directly calculates the given value of the q-axis voltage of the motor based on the constraints between the bus current command value and the motor variables, and can realize the network The power factor on the side is high, and the power factor control effect on the grid side is less affected by system parameter errors. The overall control strategy is easy to implement and the system is highly robust. The power factor control effect is shown in Figures 3 and 4. In the q-axis current convergence area, the grid-side input current is a standard sine wave, thereby maximizing the grid-side power factor.

Claims (5)

1. The control method of the electrolytic capacitor-free permanent magnet synchronous motor driving system based on bus current control is characterized by comprising the following steps of:
firstly, according to the bus current command valueConstraint conditions between the motor variable and the motor q-axis voltage set value +.>
Then the motor q-axis voltage set value is set based on Lyapunov stability theoryCarrying out convergence analysis on the current of the motor; if convergence is determined, the motor q-axis voltage given value +.>If it is judged that the current is not converged, the current is judged to be +/based on the bus current command value>The approximate relation between the motor q-axis current and the motor q-axis current obtains the motor q-axis current command value +.>And based on feedback linearization concept, obtaining motor q-axis voltage given value +.>
Finally, the motor is arrangedd-axis voltage settingq-axis voltage is given>Performing coordinate transformation to obtain voltage given value +.>Outputting the voltage to the motor;
d-axis current command value of motorBased on minimum copper loss principle calculation, motor d-axis voltage given value +.>Obtained from a current regulator; d-axis current command value of motor->As the q-axis current of the motor of the electrolytic capacitor-free driving system is a periodic sine wave, the d-axis current instruction constant value of the motor is obtained based on the principle of minimum copper loss>The calculation method comprises the following steps:
first performing Lagrangian functionWherein:
as an objective function, the copper loss of the system is expressed, wherein i d For motor d-axis current, i qrms The q-axis current effective value of the motor; />As a constraint condition of system torque, L is d ,L q D-q axis inductances of the motors respectively, < >>I is the flux linkage of a permanent magnet of the motor qav The average value of q-axis current of the motor is represented by T, and the average load torque of the motor is represented by T;the constraint condition between the effective value and the average value of the q-axis current of the motor is adopted; lambda (lambda) 1 ,λ 2 Is a Lagrangian multiplier;
then let Lagrangian function F (i d ,i qrms ,i qav12 ) The first partial derivative for each variable is equal to zero, yielding:
finally, solving the d-axis current i corresponding to the minimum copper loss control by five equation sets in the formula (1) d And takes the same as a d-axis command valueThe expression is:
obtaining the given value of the q-axis voltage of the motorThe method of (1) comprises the following steps:
firstly, the transfer function F of the inverter under a static three-phase coordinate system d Expressed as:
wherein: a is that m For the amplitude value of the modulation ratio of the inverter, theta e Leading the angle value of the phase shaft of the motor a for the motor d-axis;the angle value of the d axis of the motor is advanced for the output phase angle of the inverter;
the motor voltage u under the static three-phase coordinate system a 、u b 、u c By inverter transfer function F d And bus voltage u dc Expressed as:
[u a u b u c ] T =F d ·u dc (3);
using motor current i in a stationary three-phase coordinate system a 、i b 、i c Transfer function with inverter F d Bus current i dc Expressed as:
i dc =F d T ·[i a i b i c ] T (4);
transforming the constant amplitude value of the equation (3) and the equation (4) from a static three-phase coordinate system to a rotating two-phase coordinate system to obtain the motor voltage u under the rotating coordinate system d 、u q Bus current i dc Modulation ratio vector with inverterThe relation is as follows:
wherein: i m The current vector amplitude value of the motor;leading the angle value of the d axis of the motor for the phase angle of the motor current; />Is a motor current vector; a is that d 、A q Respectively inverter modulation ratio vector->A component in the d-q coordinate system;
then, the modulation ratio vector is plotted according to the formula (6)In the motor current vector->The calculation formula of the projection length L is as follows:
modulation ratio vectorThe coordinate values of the intersection points of the vertical line and the d-q axis coordinate system are respectively as follows:
finally, obtaining the modulation ratio vector by the method (5)D-axis component>Obtained from similar triangle relationsObtaining the motor q-axis voltage set value according to the formula (5)>
2. The control method of the electrolytic capacitor-less permanent magnet synchronous motor driving system based on bus current control according to claim 1, wherein the bus current command value is as followsAnd obtaining according to the output value of the speed regulator, the network side voltage phase and the bus capacitance value.
3. The control method of the electrolytic capacitor-less permanent magnet synchronous motor driving system based on bus current control according to claim 2, wherein the bus current command value is as followsThe calculation method comprises the following steps: firstly, the network side voltage waveform is phase-locked to obtain the network side voltage phase angle theta s
Then the motor rotating speed command value is differenced with the actual rotating speed, and the current command amplitude is input from the output net side of the speed regulatorCombining net side voltage phase angle theta s Obtaining the instantaneous value of the network side input current command +.>
Finally, inputting current command instantaneous value to network sideSubtracting the instantaneous value i of the capacitive current c Obtaining bus current command value +.>
4. The control method of the electrolytic capacitor-less permanent magnet synchronous motor driving system based on bus current control according to claim 1, wherein the motor current convergence judging method comprises the steps of: firstly, respectively representing the voltage equation of the permanent magnet synchronous motor under a d-q coordinate system as follows:
wherein: r is stator resistance; omega e Is the electrical angular velocity of the motor;
then giving the calculated motor q-axis voltageBringing a motor voltage equation (9), and simplifying to obtain:
simplifying the relation of the current of the motor d-q axis to obtain a state variable equation of the current of the motor q axis, wherein the state variable equation is as follows:
nonlinear equation stability represented by formula (11) is analyzed based on the lyapunov direct method: order theEqual to zero, two balance points exist in the system, and the two balance points are respectively:
when the system is in normal operation, the q-axis current of the motor is positive, and the positive balance point of the system is ensured, namely the system needs to meet +.>Taking positive balance point i q_0 And (3) performing convergence judgment:
for ease of analysis, y=i q -i q_0 Bringing the equation into the state space zero point of the balance point to obtain a transformed equation:
combining the formula (11) with the formula (13) to simplify the process:
construction of a positive-going Lyapunov functionEasy-to-get y > -i q_0 Derivative of Lyapunov function +.>The constant value is smaller than zero, so that the stable operation of the system can be ensured;
if the system does not meetAnd y > -i q_0 Under these two convergence conditions, the motor q-axis current command value +_is obtained from the approximate relationship between the motor q-axis current and the bus current>The motor q-axis voltage equation (9) is rewritten as: />According to the feedback linearization idea, let ∈ ->And brings the motor q-axis voltage equation into the motor q-axis voltage equation, so as to simplify +.>Let control rate->Reduced->Wherein a is a positive constant, < >>As a current error, the error between the current command and the actual current converges to zero over time.
5. The control method of a permanent magnet synchronous motor driving system without electrolytic capacitor based on bus current control according to claim 1, wherein finally, the d-axis voltage of the motor is givenq-axis voltage is given>Performing coordinate transformation to obtain voltage given value +.>And then the SVPWM module outputs the voltage to the motor.
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